Lawmakers seeking to overhaul financial industry regulations grappled Tuesday with the question of how to cover the cost of federal bailouts.

To pay for the emergency assistance provided to firms during the recent crisis, Treasury Secretary Timothy F. Geithner pressed senators to pass a tax on Wall Street and other big financial companies, arguing that the levy would discourage risky activities and help the government recoup its money.

Despite the push from the Obama administration, the prospects for the "bank tax" remain uncertain. During a congressional hearing Tuesday, Geithner said the tax provision was "an important complement" to a bill now before the Senate to overhaul financial regulations.

But some Democrats said they are reluctant to include the tax because it could complicate prospects for the hotly contested overhaul bill. They added that Sen. Max Baucus (D-Mont.), chairman of the Senate Finance Committee, is instead considering whether to include a new bank tax in a bill he plans to introduce extending some existing tax cuts.

Meanwhile, the banking committee's chairman, Christopher J. Dodd (D-Conn.), and its ranking Republican, Richard C. Shelby of Alabama, were finalizing an agreement to delete from the Senate bill a proposed $50 billion fund, financed by members of the industry, that would cover the cost of winding down large, troubled financial companies whose collapse could threaten the economy.

Republicans have criticized the provision as a "bailout fund," arguing that it would encourage financial firms to engage in overly risky behavior because they would know the money was there in the event of trouble. Under the deal reached by Dodd and Shelby, the government would recover the liquidation costs of a failing firm by selling off its assets, with the financial industry picking up any remaining costs.

Although Republican leaders had made the $50 billion fund a target of their criticism, Democrats and the administration were eager to drop it in exchange for some bipartisan support for the bill. They noted that the original idea for the fund came from Republicans, not Democrats.

The administration's bank tax proposal, however, remains in dispute.

Levy aimed at big firms

Calling it the "financial responsibility fee," Geithner said the tax would raise $90 billion over at least 10 years and could continue if the final cost of the original bailout, the Troubled Assets Relief Program, is higher than that amount. Geithner said the administration is committed to using the tax revenue to reduce the deficit.

Banks, big insurers and other kinds of financial firms with more than $50 billion in assets would face the tax, though Geithner told the Senate Finance Committee that he was open to tweaking the proposal to ensure that the fee would be applied only to the largest companies. The tax would be calculated based on the amount of liabilities a firm holds, he added. That way, a company with a riskier profile would have to pay more than conservatively managed firms.

"We designed the fee so that it would fall most heavily on firms that fund riskier activities with less stable forms of funding," Geithner told the committee. "We did look at a profits tax, and a financial transaction tax, but we thought this was a better design."

The plan faced skepticism from lawmakers, particularly Republicans. Several questioned whether the tax would unduly punish banks and crimp lending to small businesses and consumers.